735 B
735 B
| id | title |
|---|---|
| mat-04-integrals | Integrals: basics and the fundamental theorem |
Integrals
Antiderivative
An antiderivative is a function whose derivative is the integrand.
Definite integral
A definite integral measures accumulated change and is interpreted as signed area under a curve.
Fundamental theorem of calculus
The fundamental theorem connects derivatives and integrals:
- differentiation and accumulation are inverse operations (under suitable conditions)
Basic integration rules
Rules include:
- linearity
- power rule for integrals (with n not equal to -1)
- integral of 1/x is ln|x|
Substitution idea
Substitution changes variables to simplify the integrand when a composition structure appears.